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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Ellipse Law ： ウィキペディア英語版 Ellipse Law The Law of the Ellipse, or Stodola's cone law,〔Timot Veer, Andreas Ulvestad, Olav Bolland, (''FRAME, a Tool for Predicting Gas Turbine Condition as well as Reability, Availability Performance'' ), ASME/IGTI TURBOEXPO Conference 2004 June 14–17, Vienna, Austria, GT-2004-53770〕〔TU Delft (''Cycle-Tempo, Reference guide'' ), tudelft.nl, accessed 2010-11-29〕 provides a method for calculating the highly nonlinear dependence of extraction pressures with a flow for multistage turbine with high backpressure, when the turbine nozzles are not choked.〔D. H. Cooke, (''On Prediction of Off-Design Multistage Turbine Pressures by Stodola's Ellipse'' ), J. Eng. Gas Turbines Power, July 1985, Volume 107, Issue 3, 596 (11 pages), 〕 It is important in turbine off-design calculations. == Description == We consider a multistage turbine, like in the picture. The design calculation is done for design flow rate ($\backslash scriptstyle\; \backslash dot\; m\_0\; \backslash ,$, the flow expected for the most uptime). The other parameters for design are the temperature and pressure at the stage group intake, $\backslash scriptstyle\; T\_0\; \backslash ,$ and $\backslash scriptstyle\; p\_0\; \backslash ,$, respectively the extraction pressure at the stage group outlet $\backslash scriptstyle\; p\_2\; \backslash ,$ (the symbol $\backslash scriptstyle\; p\_1\; \backslash ,$ is used for the pressure after a stage nozzles, pressure does not interfere in relations here). For off-design calculations, the off-design flow rate is $\backslash scriptstyle\; \backslash dot\; m\_\; \backslash ,$, respectively the temperature and pressure at the stage group intake are $\backslash scriptstyle\; T\_\; \backslash ,$ and $\backslash scriptstyle\; p\_\; \backslash ,$ and the outlet pressure is $\backslash scriptstyle\; p\_\; \backslash ,$. Stodola established experimentally that the relationship between these three parameters represented in Cartesian coordinate system has the shape of a degenerate quadric surface, the cone directrix being an ellipse.〔Creța, p. 300〕〔Leyzerovich, p. 175〕 For a constant initial pressure $\backslash scriptstyle\; p\_\; \backslash ,$ the flow rate depends on the outlet pressure $\backslash scriptstyle\; p\_\; \backslash ,$ as an arc of ellipse in a plane parallel to $\backslash scriptstyle\; \backslash dot\; m\_\; \backslash ,0\backslash ,\; p\_\; \backslash ,$ For very low outlet pressure $\backslash scriptstyle\; p\_\; \backslash ,$, like for condensing turbines, flow rates do not change with the outlet pressure, but drops very quickly with the increase of the backpressure. For a given outlet pressure $\backslash scriptstyle\; p\_\; \backslash ,$, flow rates changes depending on the inlet pressure $\backslash scriptstyle\; p\_\; \backslash ,$ as an arc of hyperbola in a plane parallel to $\backslash scriptstyle\; \backslash dot\; m\_\; \backslash ,0\backslash ,\; p\_\; \backslash ,$. Usually, Stodola's cone do not represent absolute flow rates and pressures, but relative to the maximum flow rate and pressures, the maximum values of the diagram having in this case the value of 1. The maximum flow rate has the symbol $\backslash scriptstyle\; \backslash dot\; m\_\; \backslash ,$ and the maximum pressures at the inlet and outlet have the symbols $\backslash scriptstyle\; p\_\; \backslash ,$ and $\backslash scriptstyle\; p\_\; \backslash ,$. The pressure ratios for design flow rate at the intake and outlet are $\backslash scriptstyle\; \backslash epsilon\_0\; =\; p\_0\; /\; p\_\; \backslash ,$ and $\backslash scriptstyle\; \backslash epsilon\_2\; =\; p\_2\; /\; p\_\; \backslash ,$, and the off-design ratios are $\backslash scriptstyle\; \backslash epsilon\_\; =\; p\_\; /\; p\_\; \backslash ,$ and $\backslash scriptstyle\; \backslash epsilon\_\; =\; p\_\; /\; p\_\; \backslash ,$. If the speed of sound is reached in a stage, the group of stages can be analyzed till that stage, which is the last in the group, the remaining stages forming another group of analysis. This division is imposed by the stage working in ''limited'' (choked) mode. The cone is shifted in the $\backslash scriptstyle\; 0\backslash ,\; p\_\; \backslash ,$ axis direction, appearing a triangular surface, depending on the critical pressure ratio $\backslash scriptstyle\; \backslash epsilon\_c\; =\; p\_c\; /\; p\_\; \backslash ,$, where $\backslash scriptstyle\; p\_c\; \backslash ,$ is the outlet critical pressure of the stage group.〔Creța, p. 301〕〔Leyzerovich, p. 176〕 The analytical expression of the flow ratio is:〔Creța, p. 303〕 :$\backslash frac\}\}\; \backslash sqrt^2\; (1\; -\; \backslash epsilon\_c)^2\; -\; (\backslash epsilon\_\; -\; \backslash epsilon\_c\; \backslash epsilon\_)^2\}\}$ For condensing turbine the ratio $\backslash scriptstyle\; \backslash epsilon\_c\; \backslash ,$ is very low, previous relation reduces to: :$\backslash frac\}\}\; \backslash sqrt^2\; -\; \backslash epsilon\_^2\}\}$ simplified relationship obtained theoretically by Gustav Flügel (1885–1967).〔〔Leyzerovich, p. 174〕 In the event that the variation of inlet temperature is low, the relationship is simplified: :$\backslash frac^2\}\}$ For condensing turbines $\backslash scriptstyle\; \backslash epsilon\_2\; \backslash ,\; \backslash approx\; \backslash ,\; \backslash epsilon\_\; \backslash ,\; \backslash approx\; \backslash ,\; 0$, so in this case: :$\backslash frac\}$ During operation, the above relations allow the assessment of the flow rate depending on the operating pressure of a stage. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ellipse Law」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. 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